Many of us have watched the film by this name. I certainly like the word and its subtle meaning.
Apparently, the word came to English from a Persian fairy tale "Three Princes of Serendip" - where the princes make many fortunate accidental discoveries. More interestingly, the "Serendip" in the title is actually the Persian way of saying "Swarnadweep". Its the ancient Sanskrit name for Sri Lanka.
Etymology is cool!